In a multiple-input dynamic model, the output is a combination of the response of each of the inputs. If the system inputs are observable, meaning the process or contribution of each input can be readily known or determined, then the output may be controlled by directly changing the related inputs. However, in a large complex system, not every input is observable. For a system with unobservable inputs, because the output cannot be directly related to an input, control and optimization of the system is more difficult. A common approach to determine how each input affects the results of an output is to measure the response of a system with known multiple inputs and try to deduce a mathematical relationship between the inputs and the outputs without going into the details about how the system reacts to each individual input. This kind of approach in determining the input-output relationship is called system identification, or parameter identification.
It is noted that “input” can also be “design”. Each different “input” can be a different “design”.
The goal of performing a system identification process is to produce a result that is as close to the desired physical system output as possible by adjusting the inputs of the system. In numerical simulation applications, the parameter identification, or system identification, is to control the parametric inputs of a mathematical model, which is constructed to simulate a system, such that the output of the simulation is closely matching the system output.
In certain applications, the outputs are presented in two-dimensional (2-D) curves, for example, material properties in terms of strain-stress relationship. Generally, it is desirous for a user (e.g., engineer and/or scientist) to use a computer to generate a computed or simulated curve to match a target curve (e.g., obtained in physical specimen test), such that a computer simulation can be performed to product realistic predictions.
Matching a target curve having characteristic of monotonic increase in one coordinate is very simple, for example, using the ordinate difference between two curves as a system identification parameter.
However, matching a computed curve to a non-monotonically increased target curve is not straightforward, for example, when the target curve exhibits hysteretic behaviors. In this situation, both the target curve and the computed curve have more than one possible ordinate value for each value of the abscissa. Hence, if an abscissa value is used to find the matching value on the computed curve, the interpolated ordinate value would be non-unique.
Another problem in matching two curves is related to engineering optimization. During an iterating interim stage of optimization, the computed curve and the target curves can be completely disengaged, i.e., they do not share any common value in one coordinate of a 2-D curve. Under this situation, the optimization iteration process may become computational unstable and fails.
Therefore, it would be desirable to have an improved method and system for matching a computed curve to a target curve to enable realistic engineering simulations.